Package edu.jas.gbufd

Class SolvableSyzygySeq<C extends GcdRingElem<C>>

java.lang.Object
edu.jas.gbufd.SolvableSyzygyAbstract<C>
edu.jas.gbufd.SolvableSyzygySeq<C>
Type Parameters:
C - coefficient type
All Implemented Interfaces:
SolvableSyzygy<C>, Serializable

public class SolvableSyzygySeq<C extends GcdRingElem<C>> extends SolvableSyzygyAbstract<C>
Syzygy sequential class for solvable polynomials. Implements Syzygy computations and tests with Groebner bases.
See Also:
  • Field Details

    • logger

      private static final org.apache.logging.log4j.Logger logger
    • debug

      private static final boolean debug
    • assertEnabled

      private static boolean assertEnabled
    • sbb

      protected SolvableGroebnerBase<C extends GcdRingElem<C>> sbb
      Groebner basis engine.
  • Constructor Details

    • SolvableSyzygySeq

      public SolvableSyzygySeq(RingFactory<C> cf)
      Constructor.
      Parameters:
      cf - coefficient ring.
  • Method Details

    • resolution

      public List<SolvResPart<C>> resolution(ModuleList<C> M)
      Resolution of a module. Only with direct GBs.
      Parameters:
      M - a module list of a Groebner basis.
      Returns:
      a resolution of M.
    • resolution

      public List resolution(PolynomialList<C> F)
      Resolution of a polynomial list. Only with direct GBs.
      Parameters:
      F - a polynomial list of a Groebner basis.
      Returns:
      a resolution of F.
    • resolutionArbitrary

      public List<SolvResPart<C>> resolutionArbitrary(ModuleList<C> M)
      Resolution of a module.
      Parameters:
      M - a module list of an arbitrary basis.
      Returns:
      a resolution of M.
    • resolutionArbitrary

      public List resolutionArbitrary(PolynomialList<C> F)
      Resolution of a polynomial list.
      Parameters:
      F - a polynomial list of an arbitrary basis.
      Returns:
      a resolution of F.
    • leftZeroRelationsArbitrary

      public List<List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(int modv, List<GenSolvablePolynomial<C>> F)
      Left syzygy module from arbitrary base.
      Parameters:
      modv - number of module variables.
      F - a solvable polynomial list.
      Returns:
      syz(F), a basis for the module of left syzygies for F.
    • leftOreCond

      Left Ore condition. Generators for the left Ore condition of two solvable polynomials.
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      Returns:
      [p,q] with p*a = q*b
    • rightOreCond

      Right Ore condition. Generators for the right Ore condition of two solvable polynomials.
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      Returns:
      [p,q] with a*p = b*q
    • leftSimplifier

      Left simplifier. Method of Apel & Lassner (1987).
      Specified by:
      leftSimplifier in class SolvableSyzygyAbstract<C extends GcdRingElem<C>>
      Parameters:
      a - solvable polynomial
      b - solvable polynomial
      Returns:
      [p,q] with a/b = p/q and q is minimal and monic